US 20100103003 A1 Abstract A multi-bit (M-bit, M>1) or multi-level (nlev levels, nlev>2, encoded on M bits where M=Floor(log2(nlev))) sigma-delta analog-to-digital converter (ADC) with a variable resolution multi-bit quantizer having its resolution (number of distinct output levels) and associated quantization thresholds changed for each voltage sample with a random or pseudo-random sequence N(n) to provide automatic dynamic dithering for removing undesired idle tones in the digital output of the sigma-delta ADC. The random integer numbers N(n) between 2 and nlev may be provided by a random or pseudo-random sequence generator, e.g., Galois linear feedback shift register in combination with digital comparators and an adder.
Claims(20) 1. An apparatus for reduction of unwanted idle tones by dithering a variable resolution nlev (nlev>2) quantizer of a multi-bit (M-bit, M>1, M=Floor(log2(nlev))) sigma-delta analog-to-digital converter (ADC), comprising:
a multi-bit (M-bit, M>1) sigma-delta modulator comprising
a multi-level digital-to-analog converter (DAC),
an analog voltage summation circuit coupled to the multi-level DAC,
an analog loop filter coupled to an output of the analog voltage summation circuit,
a variable resolution quantizer having nlev (nlev>2) levels coupled to the analog loop filter,
an encoder coupled to the variable resolution quantizer, wherein the encoder converts outputs from the variable resolution quantizer into binary representations thereof and the binary representations are applied to the multi-level DAC, and
a random sequence generator coupled to the variable resolution quantizer, wherein the random sequence generator generates a plurality of random numbers N(n) in a sequence, where N(n) are random integer numbers between 2 and nlev,
whereby resolutions of the variable resolution quantizer are determined by respective ones of the plurality of random numbers N(n) for each analog voltage sample taken by the sigma-delta modulator;
a voltage reference coupled to the multi-level DAC; and a digital filter coupled to the encoder and receiving the binary representations therefrom. 2. The apparatus according to a linear feedback shift register (LFSR) having an R-bit output; a plurality of digital comparators, each of the plurality of digital comparators having a different digital threshold, an R-bit digital input coupled to the LFSR, and a digital output; and a digital adder having inputs coupled to the digital outputs of the plurality of digital comparators, and an output coupled to the variable resolution quantizer. 3. The apparatus according to 4. The apparatus according to 5. The apparatus according to 6. The apparatus according to 7. The apparatus according to 8. The apparatus according to 9. The apparatus according to 10. The apparatus according to 11. The apparatus according to 12. The apparatus according to 13. A method for reducing unwanted idle tones by dithering a variable resolution nlev (nlev>2) quantizer of a multi-bit (M-bit, M>1, M=Floor(log2(nlev))) sigma-delta analog-to-digital converter (ADC), said method comprising the steps of:
generating random numbers N(n) in a random sequence with a random sequence generator, where N(n) are random integer numbers between 2 and nlev; controlling voltage thresholds and number of distinct output levels nlev (nlev>2) of a variable resolution quantizer with the random numbers N(n); encoding outputs from the variable resolution quantizer, based upon the random numbers N(n), into binary representations thereof; controlling output voltage values from a multi-level digital-to-analog converter (DAC) with the binary representations; adding the voltage values from the multi-level DAC to input voltage samples in an analog voltage summation circuit; filtering the sum of the voltage values and the input voltage samples in an analog loop filter; and applying the filtered sum of the voltage values and the input voltage samples to the variable resolution quantizer. 14. The method according to providing a linear feedback shift register (LFSR) having an R-bit output; providing a plurality of digital comparators, each of the plurality of digital comparators having a different digital threshold, an R-bit digital input coupled to the LFSR, and a digital output; and providing a digital adder having inputs coupled to the digital outputs of the plurality of digital comparators, and an output coupled to the variable resolution quantizer, whereby the sequence of random numbers N(n) are generated. 15. The method according to 16. The method according to 17. The apparatus according to 18. The method according to 19. The method according to 20. The method according to Description This application claims priority to commonly owned U.S. Provisional Patent Application Ser. No. 61/107,820; filed Oct. 23, 2008; entitled “Method and Apparatus for Dithering in Multi-Bit Sigma-Delta Digital-to-Analog Converters,” by Philippe Deval, Vincent Quiquempoix and Alexandre Barreto; and is hereby incorporated by reference herein for all purposes; and is related to commonly owned U.S. patent application Ser. No. 12/571,892; filed Oct. 1, 2009; entitled “Method and Apparatus for Dithering in Multi-Bit Sigma-Delta Digital-to-Analog Converters,” by Philippe Deval, Vincent Quiquempoix and Alexandre Barreto. The present disclosure relates to analog-to-digital converters (ADCs) and, more particularly, to a sigma-delta ADC with a multi-bit (M-bit, M>1) variable resolution quantizer having automatic dynamic dithering for removing undesired idle tones in the digital output of the sigma-delta ADC. Analog-to-digital converters (ADCs) are in widespread use today in electronic applications for consumer, medical, industrial, etc. Typically, ADCs include circuitry for receiving an analog input signal and outputting a digital value proportional to the analog input signal. This digital value is typically in the form of either a parallel word or a serial digital bit stream. There are many types of analog-to-digital conversion schemes such as voltage-to-frequency conversion, charge redistribution, delta modulation, as well as others. Typically, each of these conversion schemes has its advantages and disadvantages. One type of analog-to-digital converter (ADC) that has seen increasing use is the sigma-delta ADC (sigma-delta and delta-sigma will be used interchangeably herein). A sigma-delta modulator typically converts an analog input to a digital serial string of “ones” and “zeros” having an average amplitude over time proportional to the analog input. Sigma-delta modulation generally provides for high accuracy and wide dynamic range as compared to earlier delta modulation techniques. Sigma-delta modulation is often referred to as an oversampled converter architecture and is typically immune from some of the earlier undesirable second order effects of delta modulation. Each sigma-delta modulator loop includes one or more quantizers that convert the analog incoming signals to a digital output code. For a sigma-delta ADC, these quantizers are low-resolution ADCs often 1-bit ADC (or comparators). In this case, the sigma-delta modulator is called a 1-bit modulator. If the output of the quantizer has a higher resolution than 1 bit, then the sigma-delta modulator is called a multi-bit modulator and the sigma-delta ADC is called a multi-bit sigma-delta ADC. In a multi-bit sigma-delta ADC, the output resolution allows more than 2 digital output levels. If the number of possible output levels (nlev) is a power of 2 (for example nlev=2̂M), the output can be encoded into an M-bit word and the modulator is a multi-bit M-bit modulator. However, the number of output levels (nlev) is not necessarily a power of 2 (especially for the low number of levels) and in this case, the modulator can also be called multi-bit or multi-level. For example, 3-level modulators are very popular. If nlev is a power of 2, an equivalent number of bits can be calculated for a multi-level modulator and is given by the formula: M=log2(nlev) where M is the number of equivalent bits. If nlev is not a power of 2, the minimum number of bits required to encode the output is: M=Floor(log2(nlev)). In a multi-level (or multi-bit) sigma-delta ADC, the quantizer is very often a Flash ADC, composed of nlev−1 comparators in parallel with equidistant thresholds of comparison, placed at (nlev−2k)/(nlev−1)*Vref where k is an integer between 1 and (nlev−1), giving an output on nlev bits coded with a thermometer coding. In that case, the number of distinct output levels is nlev which can be coded into a minimum of Floor(log2(nlev)) bits. For example, a 3-level modulator quantizer can be a Flash ADC composed of two (2) comparators with thresholds of +Vref/2 and −Vref/2 and the 3-level output words can be encoded into Foor(log2(3))=2 bits. The placement of the thresholds ensures also a uniform quantization which minimizes the quantization error average on the whole input range. In a typical flash ADC implementation, each comparator has its own switched-capacitor input stage in determining its associated voltage threshold, and a thermometer-to-binary encoder at the outputs of the flash comparators for generating the digital words to the sigma-delta modulator loop digital-to-analog converter (DAC), and a digital signal output decimation filter. All sigma-delta modulators, working in a continuous mode, produce idle tones at their outputs if a certain periodic or direct current (DC) input is provided. These idle tones are due to the quantization process and are inherent in the design of the sigma-delta modulator architecture. These idle tones are unwanted and create undesired behavior at the outputs like undesired high tones in an audio device. These tones limit the spurious free dynamic range (SFDR) and thus the signal-to-noise-and-distortion (SINAD) of the device especially if specific direct current (DC) inputs are provided (that are usually a rational fraction of the quantization step). Therefore, what is needed is a way to remove these idle tones. By “breaking” and “scrambling” the idle tones with the addition of a pseudo-random signal inside the sigma-delta modulator loop, the resulting signal may then be filtered in the loop itself to remove the idle tones, thus there is no need to add filtering at the digital output to recover the desired signal and eliminate the idle tones. One of the best locations for adding a dithering signal is at the input of the modulator quantizer. Any error at this location is re-divided by the gain of the modulator loop which is very large, and then is filtered and noise-shaped exactly like the quantization noise without any need of additional filtering circuitry. If this signal is random or pseudo-random (uncorrelated with the input), it will vary the bitstream sequence for a given input signal and break the periodicity of it due to its random nature. According to the teachings of this disclosure, in a multi-bit (or multi-level) sigma-delta ADC that has an nlev (nlev>2) resolution quantizer (in that case the nlev levels can be encoded on M bits where M=Floor(log2(nlev)), so M>1), when replacing the quantizer with a variable resolution quantizer where the resolution (number of output levels) of the quantizer varies with a random or pseudo-random sequence (named the resolution sequence), it creates a new quantization error function, depending on this sequence, which introduces an additional quantization error that will dither the incoming input signal. The added quantization error is the difference between the output of the fixed quantizer with the maximum resolution (nlev) and the output of the quantizer with variable resolution where the resolution N(n) is chosen at each sample n by a random or pseudo-random sequence N(n) (the resolution sequence) and where N(n) is an integer between 2 and nlev. When this type of dithering is added at the quantizer stage, the induced additional quantization errors will also be processed and noise-shaped by the feedback loop of the sigma-delta modulator and filtered away, thereby eliminating the need for additional output filters often necessary with other types of dithering schemes. Dithering the modulator quantizer resolution, as more fully described hereinafter, is also automatically dynamic, since the quantization error is unchanged for large absolute values of quantizer inputs no matter what resolution is chosen by the random or pseudo-random sequence. According to the teachings of this disclosure, the feedback DAC in the sigma-delta loop will always feedback the maximum output value, no matter what resolution is chosen, and therefore the variable resolution quantizer gives the same quantization error as a fixed nlev-resolution quantizer because there is no added quantization error for a maximum output value. The amount of added signal with the variable resolution quantizer is automatically lowered to no influence (introduction of error) for large signals and thereby provides very good stability performance without additional circuitry. Whereas other existing dithering techniques have to evaluate the input signals and adapt the amount of added signals to avoid saturating the quantizer inputs when large signals are present. This may require additional circuitry and cause loop instability. Implementation of signal dithering in sigma-delta ADCs, according to the teachings of this disclosure, is also simple to put in place and does not require significant additional circuitry to provide efficient tone scrambling. When starting from a multi-level (nlev) ADC it only requires minor additional circuitry to make adjustable the number of levels and the associated thresholds of the quantizer (which is often a flash ADC) so that the quantizer can vary its resolution for each sample taken. Additionally, a random or pseudo-random generator is implemented to control the resolution sequence N(n) that will vary the resolution at each sample. The resolution sequence may be any value from 2 to nlev or may be selected ones of all possible values from 2 to nlev. The resolution sequence is random or pseudo-random (e.g., uncorrelated with the input signal) so that the dithering effect is maximized. Using a larger proportion of small levels (e.g., two (2) levels) will also make the dithering more pronounced but as a side effect will increase the output quantization noise (and thus decrease SNR), and will also degrade the stability of the ADC loop. The length of the sequence in case of a pseudo-random one is determined as a function of the need for dithering low-frequency signals: a long sequence will “scramble” idle tones appearing at a lower frequency and will “smooth” further the low frequency portion of the output spectrum. The “granularity” of the sequence (number of distinct N values taken in the resolution sequence) may be freely chosen knowing that a large number of distinct levels will induce better randomness resulting in a better dithering effect. When using flash ADC quantizers, only a few additional switches are required in order to change the quantizer resolution for proper quantization resolution of the dithering sequence, according to the teachings of this disclosure. The flash ADC quantizer comprises (nlev−1) comparators in parallel, each comparator having a different comparison threshold: threshold(k), where k is an integer between 1 and (nlev−1). These comparison thresholds may be equal to: threshold(k)=(nlev−2k)/(nlev−1)*Vref which results in a uniform quantization. The comparator comparison thresholds may be defined by a switched-capacitor stage with different capacitor ratios, as more fully described hereinafter. In order to change the resolution of the flash ADC, only a group of N(n)−1 out of the total (nlev−1) comparators need be used, giving N(n) distinct output levels (resolution). If a uniform quantization is desired (less quantization error) for each N(n) in the sequence, the comparators that are chosen to be used need to have their threshold values modified accordingly so that their thresholds are equal to threshold(k,n)=(N(n)−2k)/(N(n)−1)*Vref, where k is an integer between 1 and N(n)−1. Modifying the capacitor ratios changes the thresholds of each active comparator of the flash ADC quantizer so that they are equal to their new value at each sample. Modifying capacitors ratios is possible by enabling or disabling one or more unit caps in the Cin or the Cref arrangement with appropriate switches, as more fully described hereinafter. Capacitor arrangements may be implemented so that all necessary threshold combinations are available. Furthermore, for a lower power implementation, the comparators that are not required at a given sample n (total of nlev−N(n) comparators) can be shutdown (e.g., put into a low power mode) during the sample because their outputs are not used in the feedback DAC and are thereby not taken into account when encoding the bitstream in the sigma-delta modulator. According to a specific implementation of this disclosure, when nlev=5, where N(n) is chosen between 2, 3 and 5 (N(n) is in the form of 2̂r+1, where r is an integer), and when the quantization is uniform, the DAC output levels are +Vref, +Vref/2, 0, −Vref/2 and −Vref when N(n)=5; +Vref, 0, −Vref when N(n)=3; and +Vref and −Vref when N(n)=2. Since the output levels needed when N(n)=2, 3 or 5 are the same ones as the ones of a fixed five-level DAC, e.g., the DAC in the feedback loop of the sigma-delta ADC can be implemented according to the teachings of commonly owned U.S. Pat. No. 7,102,558, entitled “Five-Level Feed-Back Digital-to-Analog Converter for a Switched Capacitor Sigma-Delta Analog-to-Digital Converter” by Philippe Deval, and is incorporated by reference herein for all purposes. This reference discloses an implementation that it is inherently linear each time, for each sample taken and for any resolution sequence. Therefore, this implementation ensures an inherent linearity and thus extremely low THD figure and higher SINAD figure while keeping the advantages of dithering and low-complexity implementation. An advantage of the dithering process disclosed herein is that the dithering has substantially no effect on large inputs signals which greatly helps for maintaining stability of the sigma-delta modulator. Another advantage of the dithering process disclosed herein is simplicity and ease of implementation with only a few additional switches to change capacitor ratios in the capacitor switched inputs of the comparators of a flash ADC implementation. Another advantage of the dithering process disclosed herein is that it also reduces total harmonic distortion (THD), because its effect on distortion, which can be considered as a specific type of idle tone, is equivalent to its effect on any other tone. It “scrambles” the harmonics with the same efficiency as if they were an idle tone coming from the quantization process even though the root cause of harmonic distortion may be different. Another advantage of the dithering process disclosed herein is that it can be easily switched off. In order to switch off the dithering process, the resolution sequence N(n) can be made equal to nlev for all samples (N(n)=nlev). According to a specific example embodiment of this disclosure, an apparatus for reduction of unwanted idle tones by dithering a variable resolution nlev (nlev>2) quantizer of a multi-bit (M-bit, M>1, M=Floor(log2(nlev))) sigma-delta analog-to-digital converter (ADC) comprises; a multi-bit (M-bit, M>1) sigma-delta modulator comprising a multi-level digital-to-analog converter (DAC), an analog voltage summation circuit coupled to the multi-level DAC, an analog loop filter coupled to an output of the analog voltage summation circuit, a variable resolution quantizer having nlev (nlev>2) levels coupled to the analog loop filter, an encoder coupled to the variable resolution quantizer, wherein the encoder converts outputs from the variable resolution quantizer into binary representations thereof and the binary representations are applied to the multi-level DAC, and a random sequence generator coupled to the variable resolution quantizer, wherein the random sequence generator generates a plurality of random numbers N(n) in a sequence, where N(n) are random integer numbers between 2 and nlev, whereby resolutions of the variable resolution quantizer are determined by respective ones of the plurality of random numbers N(n) for each analog voltage sample taken by the sigma-delta modulator; a voltage reference coupled to the multi-level DAC; and a digital filter coupled to the encoder and receiving the binary representations therefrom. According to another specific example embodiment of this disclosure, a method for reducing unwanted idle tones by dithering a variable resolution nlev (nlev>2) quantizer of a multi-bit (M-bit, M>1, M=Floor(log2(nlev))) sigma-delta analog-to-digital converter (ADC) comprises the steps of: generating random numbers N(n) in a random sequence with a random sequence generator, where N(n) are random integer numbers between 2 and nlev; controlling voltage thresholds and number of distinct output levels nlev (nlev>2) of a variable resolution quantizer with the random numbers N(n); encoding outputs from the variable resolution quantizer, based upon the random numbers N(n), into binary representations thereof; controlling output voltage values from a multi-level digital-to-analog converter (DAC) with the binary representations; adding the voltage values from the multi-level DAC to input voltage samples in an analog voltage summation circuit; filtering the sum of the voltage values and the input voltage samples in an analog loop filter; and applying the filtered sum of the voltage values and the input voltage samples to the variable resolution quantizer. A more complete understanding of the present disclosure thereof may be acquired by referring to the following description taken in conjunction with the accompanying drawings wherein: While the present disclosure is susceptible to various modifications and alternative forms, specific example embodiments thereof have been shown in the drawings and are herein described in detail. It should be understood, however, that the description herein of specific example embodiments is not intended to limit the disclosure to the particular forms disclosed herein, but on the contrary, this disclosure is to cover all modifications and equivalents as defined by the appended claims. Referring now to the drawing, the details of specific example embodiments are schematically illustrated. Like elements in the drawings will be represented by like numbers, and similar elements will be represented by like numbers with a different lower case letter suffix. Referring to The digital filter The output bitstream Referring to The random sequence generator Referring to Referring to The switched capacitor blocks A voltage reference (not shown) is also coupled to the switched capacitor blocks The plurality of comparators The switched-capacitor blocks Referring now to Each of the switched capacitor blocks A voltage reference (not shown) is also coupled to the switched capacitor blocks The plurality of comparators The nlev−1 switched-capacitor blocks Selected outputs from the plurality of comparators Referring to The random sequence generator A five-level bit stream from the output Switched-capacitor blocks for comparator When N(n)=5, all comparators When N(n)=3, only comparators When N(n)=2, only comparator Referring to Referring to When switches The output node voltage Vout is positive when Vin>¾*Vref and is negative when Vin<¾*Vref, thus the threshold is ¾*Vref. Referring to The output node voltage Vout is positive when Vin>½*Vref and is negative when Vin<½*Vref, thus the threshold is ½*Vref. Similarly, when switches Therefore by selectively turning off (open) or on (close) switches Referring to Referring to and the voltage at the output node, Out+/−, is equal to: The output node voltage Vout is positive when Vin>b/a*Vref and is negative when Vin<b/a*Vref, thus the threshold is b/a*Vref. With this configuration, any b/a*Vref threshold may be configured so long as there are enough capacitors to obtain the threshold granularity desired. Any −b/a threshold may also be obtained if the Vref+ and Vref− nodes are swapped as shown in For a uniform quantization, the threshold for the comparator k takes the form: for a fixed quantizer, and with N(n) being between 2 and nlev as disclosed herein previously. By assigning a=nlev−1 and b=Abs(nlev−2k) for a fixed quantizer, and a(n)=N(n)−1 and b(n)=Abs(N(n)−2k) for a variable quantizer, the switched capacitor block Since a(n)=N(n)−1, the number of capacitors coupled to Vin+/− through the switches Since b(n)=N(n)−2k, the number of capacitors coupled to Vref+/− through switches In order to realize a proper uniform quantization, with any N(n) number of levels, the maximum number of capacitors used in both the Vin+/− and Vref+/− arrangement is A=nlev−1 and B=nlev−2, so the total number of capacitors is 2*(nlev−1)+2*(nlev−2)=4*nlev−6. Out of these (4*nlev−6) unit capacitors of C value, the number of capacitors at each sample n in the arrangements of the switches is connected in the arrangements of switches at each sample n and for each comparator k as long as there is enough in total number of unit capacitors and associated switches that are split in the proper manner to obtain the threshold granularity desired. While embodiments of this disclosure have been depicted, described, and are defined by reference to example embodiments of the disclosure, such references do not imply a limitation on the disclosure, and no such limitation is to be inferred. The subject matter disclosed is capable of considerable modification, alteration, and equivalents in form and function, as will occur to those ordinarily skilled in the pertinent art and having the benefit of this disclosure. The depicted and described embodiments of this disclosure are examples only, and are not exhaustive of the scope of the disclosure. Referenced by
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